Answer:
minimum value of C is 46
Step-by-step explanation:
A sketch of the constraints is advised.
Sketch
4x + 3y = 24
with intercepts at (0, 8) and (6, 0)
x + 3y = 15
with intercepts at (0, 5) and (15, 0)
The solutions to both are above the lines.
Solve 4x + 3y = 24 and x + 3y = 15 simultaneously to obtain point of intersection at (3, 4)
Then the coordinates of the vertices of the feasible region are at
(0, 8), (3, 4) and (15, 0)
Evaluate the objective function at each vertex
(0, 8) → C = (6 × 0) + (7 × 8) = 0 + 56 = 56
(3, 4) → C = (6 × 3) + (7 × 4) = 18 + 28 = 46
(15, 0) → (6 × 15) + (7 × 0) = 90 + 0 = 90
The minimum value of C is 46 when x = 3 and y = 4
